#include <stdlib.h>
#include <math.h>
#include <stdio.h>
#include <float.h>

#define EPS 2*DBL_EPSILON 

typedef struct {double v; double e;} double_error;

double_error int_to_valuetype(int i){
	double_error de;
	de.v = (double) i;
	de.e = EPS*abs(i);
	return de;
}

double_error int_to_exptype(double d){
	double_error de;
	de.v = d;
	de.e = EPS*fabs(d) + DBL_MIN;
	return de;
}

bool to_string(char* s, double_error de){
	sprintf(s,"%f +/- %6.1e",de.v,de.e);
	return true;
}

double_error sum(double_error de1, double_error de2){
	double_error de;
	de.v = de1.v + de2.v;
	de.e = de1.e + de2.e + ( fabs(de1.v) + fabs(de2.v) + de1.e + de2.e )*EPS + DBL_MIN;
	return de;
}

double_error difference(double_error de1, double_error de2){
	double_error de2m;
	de2m.v = -de2.v;
	de2m.e = de2.e;
	return sum(de1,de2m);
}

bool is_greater(double_error de1, double_error de2){ return ((1+EPS)*(de1.v+de1.e) > de2.v-de2.e); }

double_error maximum(double_error de1, double_error de2){
	double_error de;
	double max1 = de1.v + de1.e;
	double max2 = de2.v + de2.e;
	if( max1 >= max2 ){
		de.v = de1.v;
		de.e = de1.e + max1*EPS + DBL_MIN;
	} else {
		de.v = de2.v;
		de.e = de2.e + max2*EPS + DBL_MIN;
	}

	return de;
}

double_error product(double_error de1, double_error de2){
	double_error de;
	de.v = de1.v * de2.v;
	double p12 = fabs(de1.v)*de2.e*(1+EPS) + DBL_MIN;
	double p21 = fabs(de2.v)*de1.e*(1+EPS) + DBL_MIN;
	double p22 = de1.e*de2.e*(1+EPS) + DBL_MIN;
	double s = (p12 + p21 + p22)*(1+2*EPS);
	de.e = s + ( fabs(de.v) + s )*EPS + DBL_MIN;
	return de;
}

double_error ratio(double_error de1, double_error de2){
	double_error de2i;
	de2i.v = 1/de2.v;
	if(de2.e > fabs(de2.v)/2) de2i.e = INFINITY;
	else de2i.e = 2*de2.e/(de2.v*de2.v) + fabs(de2i.v)*EPS + DBL_MIN; //2* is extra margin in case de2.e is near de2.v/2
	return product(de1,de2i);

}

double_error absolute(double_error de){
	double_error dea;
	dea.v = fabs(de.v);
	dea.e = de.e;
	return dea;
}

double_error power(double_error de, double_error p) {
	double_error dep;
	dep.v = pow(de.v,p.v);
	double dmin = (de.v - de.e)*(1-EPS);
	double dmax = (de.v + de.e)*(1+EPS);
	double pmin = (p.v - p.e)*(1-EPS);
	double pmax = (p.v + p.e)*(1+EPS);
	double rmin,rmax;
	if(dmin >= 1){
		rmin = pow(dmin,pmin);
		rmax = pow(dmax,pmax);
	} else if(dmax >= 1) {
		rmin = pow(dmin,pmax);
		rmax = pow(dmax,pmax);
	} else {
		rmin = pow(dmin,pmax);
		rmax = pow(dmax,pmin);
	}
	if(dmin >= 0) dep.e = rmax-rmin + 2*EPS*rmax;
	else dep.e = (1+2*EPS)*rmax;
	return dep;
}

double to_double(double_error de){ return de.v; }

bool root_to_string(char* s, double_error de, double_error p){
	double_error de1p = power(de,ratio(int_to_valuetype(1),p));
	to_string(s,de1p);
	return true;
}